Yes, the only food shop in my village, and most of the villages within about a 20 minute drive, is a Dollar General. We used to have a small independent general store, but it went out of business a couple years ago.
The larger grocery store I mentioned is a family run business about 20 miles away, and while it is usually better stocked than the omnipresent Dollar Generals, they've been short of dairy and other staples too.
The only sure way to get supplies is to drive to a Walmart or Meijer in a town about 30 miles from here.